California Fixed Gear Sablefish Fishery

The objectives of this work are the following:

  1. To model and calibrate a fishery problem using aggregate data
  2. To make the model abstract enough that most components can be reused for our future work on archetypes
  3. To make the model flexible enough that it’s easy to develop alternative scenarios and judge policy
  4. To test the importance of using more realistic assumptions and data

Here we are simulating the West Coast fixed gear sablefish fishery, in particular from 2001 onward. The catch shares program review is a great introductory read on the fishery (send your thanks to Erin).
Here’s the simplified take-away points:

In truth things are more complicated (for example the quotas are not split equally among boats but depend on a series of permits that can be stacked) but we are not trying to be super-realistic here.

We decided as a first pass to generate a simple model as follows:

Which looks like this:

Calibration

Biology has been calibrated by Kristin so that’s taken care of. We don’t have logbook data so we can’t really calibrate behaviour and we just assume standard explore-exploit-imitate. We need to calibrate 3 things:

Parameter Meaning
Hold Size The maximum amount of catches a boat can hold
Catchability Sablefish proprtion of sablefish biomass fished from a cell (\(\frac{1}{\text{kg}\times \text{hour}}\))
Catchability Yelloweye proprtion of rockfish biomass fished from a cell (\(\frac{1}{\text{kg}\times \text{hour}}\))

The issue with hold-size is that while we have some data on vessel length, here we are really looking to generate the “average boat” which doesn’t actually exist. Moreover while sablefish is the main target, there are other bycatch species besides yelloweye and we simulate this indirectly by assuming a smaller hold size than what is realistic.
For our Gulf of Mexico work we assumed a long-liner maximum hold-size was 6500kg (which was the 95th percentile of landings from the logbook data) so we are looking in that neighborhood as well.

Catchability for sablefish and yelloweye also need to be calibrated in our model. Catchability \(q\) solves the following: \[ q \cdot \text{Effort} \cdot \text{Biomass} = \text{Catches} \] \[ q= \frac{\text{Catches} }{\text{Effort} \cdot \text{Biomass}} \] However in a geographical model it’s pointless to solve this equation because our agents can only ever catch biomass in a cell, not biomass in general and cells are not explored uniformly. If we fix which cells are visited and when we could substitute \(\text{Biomass}\) with something like \(\text{Cell Biomass}\) but that wouldn’t work in an adaptive agent-based model because agents go to different cells depending on \(q\) so that as soon as we fix \(\text{Actual Biomass}\) the cells visited change making it the whole process pointless (now, if we had logbook data…).

Now calibration itself is not too hard, we simply need to use our usual optimiser trying to change our three parameters to minimise distance from data. The key is to pick which data to calibrate against.

We know sablefish landings until 2011 but we can’t use them. Pre-2001 the rules changed too fast and dramatically so that we would need to code each of them in and post-2001 the landings are fixed by quota so that any absurdly high sablefish catchability would work and zero the distance from data.

We can however use yelloweye catches from 2001 but we need to assume that stock assessment guesses are correct (since yelloweye is always discarded) and that all commercial catches of yelloweye are due to fixed gear. This means our model should produe about 5.43mt of yelloweye bycatch a year. Moreover we can use 2011 observations on profits made in the fishery according to the catcher-vessel report, where it assumes an average profits of 10994.29$ (deflated to 2001 $).

The error then would look \[ \text{error} = \sum_{t=2001}^{2011} (\text{Yelloweye catches}_{t} - 5.43 ) + \text{Average Profits}_{2011} - 10994.29 \] Except we want to divide each element by the empirical standard deviation (to weigh our uncertainty).

We feed this score function to the optimiser and it spits out:

Parameter Value
Hold Size 7463.44 kg
Catchability Sablefish 0.000200
Catchability Yelloweye 0.000142

Which is neat. Notice that yelloweye catchability is quite high. This is because in our model most of the yelloweye habitat is protected which means that boats only infrequently ever risk picking up yelloweyes. This implies that in order to generate 5 tonnes of catches each year the probability of catching yelloweye when it is under the boat has to be high.

We can take a look at distance from reality of the calibrated model. This histogram plots the yelloweye catches from 2001 to 2011 for 250 simulated runs.

We are a bit off on the profit side however:

But this is not too worrying since standard deviation on that observation is about 15,000$ so that the weighted error is very low.

Policy-making

Status Quo

We now have a fishery simulator, we can use it to guess what happens as policies are introduced.

First of all it is interesting to study what happens if we run the simulation for 60 years when regulations are unchanged. First, average profits slowly decrease over time

More worrying, the yelloweye discard increases steadily.

Fortunately however both biomasses are increasing over time.

Biomass will increase simply because the system is very strictly regulated. However what is puzzling is that profitability goes down even though there is a lot more fish to catch.

One clue here is that both the average and the standard deviation of distance from port goes up over time:

That is, fishers are still facing local depletion even though biomass is growing. They are answering it in average by going further from port.

This means that the movement parameter for Sablefish is fundamental (as it is the main driver for local depletion) and determines to a great extent long-term profitability of the fishery.

Comparing policies

Here’s a few things we can try to do:

  1. What if we switch the IQ with a proper ITQ ?
  2. If we do impose an ITQ, should the RCA stay or go?
  3. Should the ITQ be single specied or multi-specied? (so should there be a market for Yelloweye quotas) ?
  4. Would we be better served by having separate quota markets for each state?

When we look at profitability, it turns out that moving from single species IQ to ITQ has absolutely no effect while the RCA is still on. This was somewhat predictable since we haven’t really modelled boat heterogeneity so gains from trade are somewhat limited.

ITQ itself also does not significantly reallocates resources from one state to the other.

What happens if we take away the RCA as well? There are really two ways around it:

  1. We can just take out the RCA while creating an ITQ
  2. We can take out the RCA but substitute it with a 2 species ITQ where 5mt of yelloweye fish quota are distributed

For obvious reasons the first option is far more profitable, both in the short and the long run. It opens up the entire coast, especially areas near port, to exploitation but without observers on boat the only cost of fishing in previously protected areas is the time spent discarding Yelloweye.

We can double-check this narrative by looking at simulated yelloweye discards:

Fortunately these catches would still not be enough to derail yelloweye recovery over the long run, as shown in the next figure. It should be the policy-maker to decide whether this tradeoff is worth it.

We can compare these results with imposing a fully specified 2-species ITQ with observers on board and no discards allowed. Profits are lower in the short run, but slightly higher in the long run and more consistent.

It is however a mistake into thinking that the ITQ replicates the behaviour of the MPA; we can see this by looking at distance from port.
The 2 species ITQ with discard ban has fishers catching quite close to port; that however is where yelloweye lives. What is going on?

It’s not a failure of the ITQ since quota prices are doing their jobs at disincentivating yelloweye catches as shown in the next figure. Yelloweye is worth 0 to sell by assumption so any positive quota price is automatically a fine. The first year some simulation have yelloweye quota costing 80$ a kg but over 60 years the average goes to about 1.31$ a kg.

The key to understanding this dynamic is provided by the sablefish landings: unlike the previous policies, the 2 species ITQ system often fails to achieve 100% attainment rate of sablefish quota. The key here is that fishers forego some of the sablefish landings and incur in some of the yelloweye costs just in order to fish nearer to port where costs are lower.

Regional Management

So far we have assumed that yelloweye rockfish is a single stock, uniformly distributed in its area. What if that’s not the case and Washington’s yelloweye is a separate stock with same parameters but different virgin biomass?
From the biological fits Kristin has done it turns out that Yelloweye biomass is much lower in Washington and while that is due mostly because of less overfishing it is this current difference in stock that drive most of the following results.

I try 4 different combinations:

It turns out that state-wide ITQs have only a negligible effect on behaviour of the agents and the model. This is because in our simplified world there is really nothing differentiating Oregon fishers from Washington ones.

In general the main dynamic generated is similar to the ITQ scenario described in the previous section: boats give up on some sablefish quota in order to fish closer to port in previously protected areas until yelloweye quotas are exhausted. The difference is that Washington fishers have an advantage now because they fish much less yelloweye for each unit of sablefish, thereby reducing wasted sablefish quota.

First we can look at average profits made per port per year:

Which shows how with two separated stocks Washington has an edge in terms of profits. This is given by the fact that Washington fishers aggressively fish nearer to port in the first years of simulation. This is only temporary however because a combination of local depletion of Sablefish together with increasing yelloweye quota prices (given in part by demand from other states) push Washington boats further out; they however retain the advantage of needing less yelloweye quotas than fishers from other states.

The overall increase in profits is primarilly due to fewer sablefish quotas being wasted compared to single stock scenarios, as shown here (total quotas is the red line):

Better Geography

The model presented here was very bare-bones. Obviously given time and resources we can make it more realistic if that’s our objective but here I am more interested in testing the sensitivity analysis of some of our assumptions. We could consider this a simple case of data-degradation (in reverse, I suppose).

What if we had decent geographical observations to improve our model? This means both a better map of the world (which is obviously easy to get) but also a good idea of where the fish actually lives. Here I recycle the bathymetry and the EFH density maps from our validation model and use them to allocate our Deriso-Schnute biology.

Assuming still only one port per state, and MPAs covering all areas with depth lower than 200m, we get a model that looks like this:

We need to recalibrate this model since the fishing opportunities are different, but the process is exactly the same as described above. The average error is a little higher than the very abstract model above, in particular regarding yelloweye catches:

But the bias to profit prediction is lower:

How different are our conclusions from what we did before? In both cases profits fall, but in the geographic scenario the fall is more pronounced:

Also in both cases yelloweye discards go up, but this is again more extreme in the case of realistic geography.

However the profit dynamics are not due to a general increase in distance to port when the geography is realistic, but just to the depletion of local good spots. However in a way “distance” in the abstract model is there precisely to coarsly rank spots into good and bad by distance when we don’t have good density maps so that the effect is the same.

Geography really starts mattering when we are dealing with distribution of income however, as shown in the next picture. The major assumption of the abstract model is the uniform distribution of fishing opportunities between ports, something that isn’t true when we use a more empirical approach. For the first few years with realistic geography the lion share of profits go to Oregon, but as those fishing spots get locally depleted, they become harder to replace while California and Washington have an abundance of secondary spots to tap.

Lessons Learned

One important lesson learned from this exercise is the strong effect of fish diffusion rates on model results. Low movement rates mean local depletion which fishers adapt to by changing their fishing spots every few years. This in turn generates falling profitability even when the overall fishable biomass is increasing.
In future we should treat movement rate as another variable to calibrate on our end, much like catchability and hold size.

One weakness exposed by this scenario is that learning rate of the agents is slow when regulations are very strict. In this particular scenario seasons last less than 30 days and only comprise a few trips. Since our agents learn by trial and error, there is only so much trial and error they can accomplish in one go. This may be unavoidable and an unwanted consequence of strict policies but it is definitely something to take into account.

We also showed how abstract geography may be enough to understand the general aggregate dynamics that motivate the fishery but may be not sufficient when studying the proper allocation of profits among different ports and states.